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Designing Kerr interactions using multiple superconducting qubit types in a single circuit

ABSTRACT

The engineering of Kerr interactions has great potential for quantum information processing applications in multipartite quantum systems and for investigation of many-body physics in a complex cavity-qubit network. We study how coupling multiple different types of superconducting qubits to the same cavity modes can be used to modify the self- and cross-Kerr effects acting on the cavities and demonstrate that this architecture could provide significant benefits for quantum technologies.
Using both analytical perturbation theory results and numerical simulations, we first show that coupling two superconduting qubits with opposite anharmonicities to a single cavity enables effective self-Kerr interaction to be diminished, while retaining the number splitting effect that enables control and measurement of the cavity field. We then demonstrate that this reduction of the self-Kerr effect can maintain the fidelity of coherent states and generalised Schr\"{o}dinger cat states much longer than typical coherence times in realistic devices. Next, we find that the cross-Kerr interaction between two cavities can be modified by coupling them both to two different qubit devices. Using a tunable intermediary qubit, we can control the strength of entangling interactions between two cavity modes on demand and achieve much better isolated cavity states.
Finally, we discuss the feasibility of producing an array of a cavities and qubits where intermediary and on-site qubits can tune the strength of self- and cross-Kerr interactions across the whole system. This architecture could provide a way to engineer interesting many-body Hamiltonians and a useful platform for quantum simulation in circuit quantum electrodynamics.